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Some Topological Properties of the Spectrum of Prime D-Filters of Distributive Lattices

A. P. Phaneendra Kumar *, M. Sambasiva Rao **, K. Sobhan Babu ***

* Department of Mathematics, Vignan's Institute of Engineering for Women, Vishakapatnam, Andhra Pradesh, India.

** Department of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra Pradesh, India.

*** Department of Mathematics, JNTU-K University College of Engineering, Guntur, Andhra Pradesh, India.

Periodicity:January - June'2021
DOI : https://doi.org/10.26634/jmat.10.1.18165

Abstract

Some properties of prime D-filters of distributive lattices are studied with respect to the direct products and set-theoretic intersection. Properties of minimal prime D-filters of distributive lattices are studied. Some topological properties of the space of all minimal prime D-filters of a distributive lattice are studied. Finally, it is showed that the space of all minimal prime D-filters of a distributive lattice is a Hausdorff space.

Keywords

Dense Element, Flter, D-filter, Prime D-filter, Direct Product, Hausdorff Space.

How to Cite this Article?

Kumar, A. P. P., Rao, M. S., and Babu, K. S. (2021). Some Topological Properties of the Spectrum of Prime D-Filters of Distributive Lattices. i-manager's Journal on Mathematics, 10(1), 22-31. https://doi.org/10.26634/jmat.10.1.18165

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